It is given that in a triangle ABC, a line from A to BC intersects BC at point D. If the ratio in which AD divides BC is given can we say anything about the ratio of areas of triangle ABD and triangle ADC ?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
Yes we can find the ratio of the areas of the two triangles.
Area of $\triangle ADC$=$$(AD\times DC\times\sin\theta)\over2$$ Area of $\triangle ABD$=$$(AD\times DB\times \sin(180^\circ-\theta))\over2$$ [$\theta$ is the angle $ADC$]
Divide these two equations and use the ratio you have to get the answer.